A Simple Axiomatization of Binary Rank-Dependent Utility of Gains (Losses)

For binary gambles composed only of gains (losses) relative to a status quo, the rank-dependent utility model with a representation that is dense in intervals is shown to be equivalent to ten elementary properties plus event commutativity and a gamble partition assumption. The proof reduces to a (difficult) functional equation that has been solved by Aczél, Maksa, and Páles (in press).